Strength of a brittle solid

The strength of a brittle solid is defined as the applied thrust force required to produce cracks in the sample under test, with uniform stress action. From the energy balance of Griffith (1980), we get the basic expression... 

Griffith criterion The Griffith criterion states that the fracture strength of a brittle solid is solely determined by its elastic properties, its surface tension and the crack or flaw size being in the material... 

The state of the surface of a brittle solid has been found to exert a considerable influence on the mechanical behaviour observed it is at least as important as the underlying molecular constitution in this regard. The presence of microscopic scratches, voids, or other imperfections will seriously weaken the tensile strength of specimens of glassy polymer, such as poly(methyl methacrylate) at ambient temperatures. 

If a solid has no surface or internal flaws (a perfect lattice), it should have very high strength. Various theoretical equations for this ultimate strength S of a brittle solid have been proposed one is [16]... 

Under ordinary application of a tensile stress, glass acts like a brittle solid. There is no observable plasticity unless the stress is highly concentrated in a localized region, such as when a microindenter is used. It may be shown that the strength brittle solid, i.e., the tensile stress required to separate two atoms a distance a apart initially, is given by... 

Brittle fracture may be considered, therefore, as two layers of atoms being pulled apart until the interatomic forces fall below their maximum (Fig. 8.82). Using this information it is possible to calculate the fracture strength of a perfect crystalline solid (a,h), e.g. 

Just as metals can be ductile or brittle, so can organic materials. The Brittle Fracture Index is a measure of the brittleness of a material. It is a measure of the ability of a compact of material to relieve stress by plastic deformation. The Brittle Fracture Index (BFI) is determined [29,31] by comparing the tensile strength of a compact, stress concentrator) in it, o-T0, using the tensile test we have described. A hole in the center of the compact generally weakens a tablet. If a material is very brittle, theoretical considerations show that the tensile strength of a tablet with a hole in it will be about one-third that of a solid tablet. If, however, the material can relieve stress by plastic deformation, then the strength of the compact with a hole in it will approach that of a compact with no hole. The Brittle Fracture... 

An impact modifier is a rubber phase dispersed in particulate form throughout the matrix of a polymer solid. Unlike plasticizers, the rubber particles retain their intrinsic properties as a separate phase. The glass transition temperature of the parent matrix is not lowered by the addition of an impact modifier. The rubber particles do two things to the parent matrix phase (2,3,4) they act as stress concentrators (i.e., a large strain will start in the matrix near the interface) and they enhance the multi-axiality in stress. As multiaxial tensile strength near the interface further enhances dilatation, which shortens the mechanical relaxation time, the otherwise brittle polymer solid of the matrix will undergo plastic deformation in the vicinities of the rubber particles. 

T is associated with the creation of a new surface. Therefore the energy spent during the application of the stress must be equal to the energy of the surface created. Orowan (1934) showed that the theoretical strength of a perfectly brittle solid is given by... 

Ashby M T, Hallam S D. The Failure of Brittle Solids Containing Small Cracks under Compressive Stress States. Acta Metall, 1986, 34(3) 497-510. Kemeny I, Cook N G W. 1986. Effective Moduli, Non-linear Deformation and Strength of a Cracked Elastic Solid. Int. J. Rock. Mech. Sci. 

Effect of RMM on the tensile impact strength of linear polyethylene. A normal polymer with a distribution of RMM was split into a number of fractions each fraction had a particular RMM. The tensile impact strength of each fraction was measured. The tensile impact strength increases with RMM. The experiment quantifies the common experience that paraffin wax (which can be looked upon as a polyethylene with less than 200 CHj units in the molecule) is a brittle solid, with a toughness incomparably less than that of polyethylene. (After L. H. Tung. S. P. E. Conference Proceedings (1958) p. 959.)... 

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